Non-Abelian gravitating solitons with negative cosmological constant

TL;DR

This paper explores the space of static, spherically symmetric Einstein-Yang-Mills solutions with negative cosmological constant, revealing new stable solutions and analyzing their stability properties through combined numerical and analytical methods.

Contribution

It provides a detailed analysis of the moduli space of solutions, clarifies stability issues, and identifies regions with different instability types, including stable solutions and sphalerons.

Findings

Identification of stable solutions with negative cosmological constant.

Clarification of stability properties and instability regions.

Determination of boundaries between different stability regimes.

Abstract

Static, spherically symmetric solutions with regular origin are investigated of the Einstein-Yang-Mills theory with a negative cosmological constant $\Lambda$. A combination of numerical and analytical methods leads to a clear picture of the `moduli space' of the solutions. Some issues discussed in the existing literature on the subject are reconsidered and clarified. In particular the stability of the asymptotically AdS solutions is studied. Like for the Bartnik-McKinnon (BK) solutions obtained for $\Lambda=0$ there are two different types of instabilities -- `topological' and `gravitational'. Regions with any number of these instabilities are identified in the moduli space. While for BK solutions there is always a non-vanishing equal number of instabilities of both types, this degeneracy is lifted and there exist stable solutions, genuine sphalerons with exactly one unstable mode and so on. The boundaries of these regions are determined.